I am trying to factor a 4th degree polynomial that does not have any rational roots. I need to somehow get it factored into two quadratics. Anyone know of a method to use.

3x^4 - 8x^3 - 5x^2 + 16x - 5

Two of the irrational roots are 1.135.. and 0.382.. but that won't help you with the factoring.

You might try factoring the fourth order polynomial into two quadratics of the form
(3x^2 + ax + b)(x^2 + cx + d)
and picking a, b, c and d to get the coefficents in the fourth order polynomial to agree. For example,
bd = -5
3c + a = -8
ad + bc = 16
3d + b + ac = -5

Where did you get that form of factoring? I have never seen any books that address factoring a fourth degree polynomial like the one I presented.

Thank you very much.

I got it from your suggestion that it be factored into quadratics. I got the two real roots by essentially graphical means. There is a specific formula for the roots of fourth order polynomials, but it is very long and complicated. I think they are hoping you will find it by trial and error.

I could understand getting the roots by graphical means if the book had put the answers in decimal form. However, they had the answers in exact form and I knew the only way to get them would be by solving a quadratic equation. Thanks once again for your help.

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